\select@language {english}
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\select@language {german}
\select@language {english}
\contentsline {chapter}{Acknowledgements}{vii}{section*.1}
\contentsline {chapter}{Abstract}{ix}{section*.2}
\contentsline {chapter}{Outline of the Thesis}{xiii}{section*.4}
\contentsline {part}{\numberline {I}Introduction and Theory}{1}{part.1}
\contentsline {chapter}{\numberline {1}Introduction}{3}{chapter.1}
\contentsline {chapter}{\numberline {2}Theory}{5}{chapter.2}
\contentsline {section}{\numberline {2.1}Diffraction}{5}{section.2.1}
\contentsline {subsection}{\numberline {2.1.1}Fresnel Diffraction}{5}{subsection.2.1.1}
\contentsline {subsection}{\numberline {2.1.2}Fraunhofer Diffraction}{5}{subsection.2.1.2}
\contentsline {section}{\numberline {2.2}Typical Ptychography setup}{6}{section.2.2}
\contentsline {section}{\numberline {2.3}Ptychographic reconstruction algorithms}{6}{section.2.3}
\contentsline {subsection}{\numberline {2.3.1}Statistics-unaware iterative reconstruction methods}{7}{subsection.2.3.1}
\contentsline {subsection}{\numberline {2.3.2}Statistical treatment: Maximum-Likelihood formulation of Ptychography}{8}{subsection.2.3.2}
\contentsline {section}{\numberline {2.4}Finite difference}{8}{section.2.4}
\contentsline {part}{\numberline {II}Main Part}{11}{part.2}
\contentsline {chapter}{\numberline {3}Refining subpixel displacements - an EM-approach}{13}{chapter.3}
\contentsline {subsection}{\numberline {3.0.1}E-step}{14}{subsection.3.0.1}
\contentsline {subsection}{\numberline {3.0.2}M-step}{14}{subsection.3.0.2}
\contentsline {chapter}{\numberline {4}Simulations}{17}{chapter.4}
\contentsline {section}{\numberline {4.1}Probe preparation}{17}{section.4.1}
\contentsline {section}{\numberline {4.2}Preparation of the simulated data}{17}{section.4.2}
\contentsline {section}{\numberline {4.3}Small biological sample}{17}{section.4.3}
\contentsline {section}{\numberline {4.4}Experimental Data}{17}{section.4.4}
\contentsline {part}{\numberline {III}Conclusion}{21}{part.3}
\contentsline {part}{Appendix}{25}{part*.8}
\contentsline {chapter}{\numberline {A}Detailed Descriptions}{25}{appendix.A}
\contentsline {chapter}{Bibliography}{27}{appendix*.9}
